Biomedical Engineering Reference
In-Depth Information
when the layer exists on the sample surface. Then, knowing the complex refractive index
N
of the formed layer, one can solve the
z
(double of the layer thickness) from equation 9.
As the ellipsometry measurement are done in air, measurements of protein layers should be
performed as fast as possible (at least within half an hour), because the drying could have
denaturating effects on the proteins.
3.2 Coherent and noncoherent response of DOE sensor
The analysis of DOE image consist of calculating the non-coherent, equation 10, and coherent,
equation 11, part of the optical signal, which relate to permittivity and optical roughness,
respectively as follows (Silvennoinen, Peiponen & Myller, 2008)
n
SW
∑
i
SW
=
m
SW
∑
j
SW
=
1
n
SW
m
SW
I
NC
=
I
i
SW
,
j
SW
−
I
C
,
(10)
1
1
where
I
C
is the coherent portion of the optical signal being
n
pk
∑
i
pk
=
m
pk
∑
j
pk
=
1
n
pk
m
pk
I
C
=
I
i
pk
,
j
pk
.
(11)
1
1
In equations 10 and 11
I
i,j
denotes the irradiance of reflected probe beam,
n
SW
and
m
SW
are
the total numbers of sensor pixel dimensions in signal window (SW),
n
pk
and
m
pk
denotes the
respective pixel dimension of each of the 16 peaks (pk) in the DOE image. Gloss
G
measured
in gloss units (GU) is standard measure for optical characterization of a surface.
Gloss is
a function of three different variables: permittivity (
, connected to
N
), angle of incidence
(
θ
i
) and topography (roughness). Gloss values are calculated from the DOE image when the
coherent response, the CCD values of the peaks, is removed from the CCD values of the DOE
image (equation 10). DOE image is produced from the irradiance of the reflected probe beam
and because of that, this calculation removes the phase information from this beam, leaving
the information (
I
NC
) of the surface reflectance and thus
and
N
. The calculated
I
NC
for the
surface (
I
NCs
) values are normalized with the non-coherent response from black glass
I
NCr
,
resulting the gloss value to be as follows
I
NCs
I
NCr
×
=
G
100.
(12)
In turn, the optical roughness (
R
opt
) values can be calculated from the DOE image utilizing
the equation 11. The
I
C
values contain the phase information of the reflected probe beam.
When the probe light beam is reflected from rough surface, the initial coherence degree of the
wave front decreases and distortion appears in DOE image 4
×
4peaks(
I
C
values). Finally, the
optical roughness
R
opt
values can be calculated from the following equation
log
e
1
4
−
R
s
I
Cs
I
Cr
R
opt
=
−
,
(13)
1
−
R
r
π
where
R
is reflectance calculated from complex refractive index (
N
)valuesmeasuredby
variable angle spectro-ellipsometer (VASE),
is the wave length of the probe beam, and the
subscrips s and r denote sample and reference respectively.
R
opt
changes of the investigated
surfaces can be determined with accuracy of 0.2 mm (in liquid), which is the detection
limit of this one-arm interferometer and reasonable sensitivity to detect nanoscale changes
appearing in the bioenvironments (Silvennoinen, Hason, Vetterl, Penttinen, Silvennoinen,
λ
